If I install this addon, will this notification icon(bell and mail) be created?

This depends on the theme you're using. If you use the theme developed especially for the BuddyPress it'll work fine. E.g. you can use the BuddyX. You can find it here: https://wordpress.org/themes/buddyx/

Also, is there a demo site where I can test it or see it directly after login?

I'm really sorry, but there isn't any website you can check it.  

As you know, this image is in the description of addon. The image is displaying the icon accurately. This is a very interesting fact for me. So I want to look at the image and see if this is possible. I'm interested in showing the icon on the site head. In other words, this becomes my purchasing standard.

And the site you mentioned already shows the icon even without this addon. So installing this addon doesn't mean it's new. That is why I want to confirm.

When I install this addon, by default, the site head must have an icon, but if the theme is incompatible with BuddyPress, it may not appear. Is this how I understand it?

Or is it only displayed for themes with BuddyPress icon on the site head like the one you mentioned?

My theme(=Mylisting) is compatible with BuddyPress. However, no notifications are displayed on the site head.